%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP256-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:28:29 AM UTC 2026
% Result : Unsatisfiable 21.97s 3.25s
% Output : CNFRefutation 21.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 14
% Syntax : Number of formulae : 132 ( 24 unt; 0 def)
% Number of atoms : 388 ( 387 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 448 ( 192 ~; 256 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(prove_this_1,axiom,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_8,axiom,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_19,axiom,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_26,axiom,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_28,axiom,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_43,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( inverse(VAR_6) != sk_c9
| multiply(VAR_6,sk_c9) != VAR_5
| multiply(sk_c9,VAR_5) != sk_c8
| inverse(VAR_4) != sk_c8
| multiply(VAR_4,sk_c8) != sk_c9
| inverse(VAR_3) != sk_c10
| multiply(VAR_3,sk_c10) != sk_c9
| multiply(VAR_2,sk_c9) != sk_c8
| inverse(VAR_2) != sk_c8
| inverse(VAR_1) != sk_c9
| multiply(VAR_1,sk_c9) != sk_c8
| inverse(VAR_0) != sk_c10
| multiply(VAR_0,sk_c10) != sk_c9 ),
file('theBenchmark.p',prove_this_43) ).
cnf(c_46,plain,
( inverse(V6) != sk_c9
| multiply(V6,sk_c9) != F
| multiply(sk_c9,F) != sk_c8
| inverse(E) != sk_c8
| multiply(E,sk_c8) != sk_c9
| inverse(D) != sk_c10
| multiply(D,sk_c10) != sk_c9
| multiply(C,sk_c9) != sk_c8
| inverse(C) != sk_c8
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(clausify,[status(thm)],[prove_this_43]) ).
cnf(c_4107,plain,
( inverse(F) != sk_c9
| multiply(F,sk_c9) != E
| multiply(sk_c9,E) != sk_c8
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(C,sk_c9) != sk_c8
| inverse(C) != sk_c8
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_46]) ).
cnf(c_47,plain,
( inverse(F) != sk_c9
| multiply(F,sk_c9) != E
| multiply(sk_c9,E) != sk_c8
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c9
| multiply(C,sk_c9) != sk_c8
| inverse(C) != sk_c8
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_4107]) ).
cnf(c_53,plain,
( inverse(E) != sk_c9
| multiply(E,sk_c9) != D
| multiply(sk_c9,D) != sk_c8
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c9
| inverse(B) != sk_c8
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_47]) ).
cnf(c_66,plain,
( multiply(B,sk_c9) != D
| multiply(sk_c9,D) != sk_c8
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c9
| inverse(B) != sk_c8
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_53]) ).
cnf(c_78,plain,
( multiply(B,sk_c9) != C
| multiply(sk_c9,C) != sk_c8
| multiply(B,sk_c8) != sk_c9
| inverse(B) != sk_c8
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_66]) ).
cnf(c_4108,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4109,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_4108]) ).
cnf(c_82,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_4109]) ).
cnf(c_111,plain,
( multiply(sk_c10,sk_c1) = identity
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_148,plain,
( multiply(sk_c9,sk_c6) = identity
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_161,plain,
( multiply(sk_c9,sk_c2) = identity
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_29,c_2]) ).
cnf(c_164,plain,
( multiply(sk_c9,sk_c2) = identity
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(paramod,[status(thm)],[c_30,c_2]) ).
cnf(c_167,plain,
( multiply(sk_c9,sk_c2) = identity
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_31,c_2]) ).
cnf(c_215,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_82]) ).
cnf(c_254,plain,
( multiply(inverse(sk_c9),sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_22,c_82]) ).
cnf(c_301,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_82,c_82]) ).
cnf(c_302,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_301,c_215]) ).
cnf(c_361,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_302,c_2]) ).
cnf(c_4110,plain,
( multiply(identity,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(identity,sk_c8) != sk_c9
| inverse(identity) != sk_c8
| identity != sk_c9
| multiply(identity,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_361,c_78]) ).
cnf(c_4111,plain,
( multiply(identity,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(identity,sk_c8) != sk_c9
| inverse(identity) != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_4110]) ).
cnf(c_4112,plain,
( multiply(identity,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(identity,sk_c8) != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_361,c_4111]) ).
cnf(c_4113,plain,
( multiply(identity,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_4112]) ).
cnf(c_4114,plain,
( sk_c9 != B
| multiply(sk_c9,B) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_4113]) ).
cnf(c_4115,plain,
( sk_c9 != B
| multiply(sk_c9,B) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_4114]) ).
cnf(c_418,plain,
( sk_c9 != B
| multiply(sk_c9,B) != sk_c8
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_4115]) ).
cnf(c_4116,plain,
( multiply(inverse(sk_c10),identity) = sk_c1
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_111,c_82]) ).
cnf(c_422,plain,
( inverse(sk_c10) = sk_c1
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_302,c_4116]) ).
cnf(c_425,plain,
( multiply(sk_c1,sk_c10) = identity
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_422,c_2]) ).
cnf(c_4117,plain,
( sk_c9 != identity
| sk_c9 != sk_c8
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_302,c_418]) ).
cnf(c_4118,plain,
( sk_c9 != identity
| sk_c8 != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_4117]) ).
cnf(c_4119,plain,
( identity != sk_c9
| sk_c8 != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_4118]) ).
cnf(c_4120,plain,
( identity != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_4119]) ).
cnf(c_557,plain,
( identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_4120]) ).
cnf(c_4121,plain,
( identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10
| identity != sk_c9 ),
inference(paramod,[status(thm)],[c_2,c_557]) ).
cnf(c_596,plain,
( identity != sk_c8
| sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10
| identity != sk_c9 ),
inference(copy,[status(thm)],[c_4121]) ).
cnf(c_4122,plain,
( multiply(inverse(sk_c9),identity) = sk_c2
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_167,c_82]) ).
cnf(c_787,plain,
( inverse(sk_c9) = sk_c2
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_302,c_4122]) ).
cnf(c_792,plain,
( multiply(sk_c9,sk_c6) = identity
| inverse(sk_c9) = sk_c2 ),
inference(paramod,[status(thm)],[c_787,c_2]) ).
cnf(c_4123,plain,
( inverse(sk_c4) = sk_c10
| identity = sk_c9
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_425,c_5]) ).
cnf(c_975,plain,
( identity = sk_c9
| inverse(sk_c4) = sk_c10 ),
inference(copy,[status(thm)],[c_4123]) ).
cnf(c_987,plain,
( multiply(sk_c10,sk_c4) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_975,c_2]) ).
cnf(c_4124,plain,
( multiply(inverse(sk_c10),identity) = sk_c4
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_987,c_82]) ).
cnf(c_1010,plain,
( inverse(sk_c10) = sk_c4
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_302,c_4124]) ).
cnf(c_1039,plain,
( multiply(sk_c4,sk_c10) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1010,c_2]) ).
cnf(c_4125,plain,
( identity = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1039,c_4]) ).
cnf(c_1110,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_4125]) ).
cnf(c_4126,plain,
( identity = sk_c9
| inverse(sk_c1) = sk_c10
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1039,c_11]) ).
cnf(c_1111,plain,
( inverse(sk_c1) = sk_c10
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_4126]) ).
cnf(c_1144,plain,
( multiply(sk_c10,sk_c1) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1111,c_2]) ).
cnf(c_4127,plain,
( multiply(inverse(sk_c10),identity) = sk_c1
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1144,c_82]) ).
cnf(c_1442,plain,
( inverse(sk_c10) = sk_c1
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_302,c_4127]) ).
cnf(c_1468,plain,
( multiply(sk_c1,sk_c10) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1442,c_2]) ).
cnf(c_4128,plain,
( identity = sk_c9
| identity = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1468,c_1110]) ).
cnf(c_4129,plain,
( identity = sk_c9
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_4128]) ).
cnf(c_1934,plain,
identity = sk_c9,
inference(copy,[status(thm)],[c_4129]) ).
cnf(c_2318,plain,
( multiply(sk_c9,sk_c6) = sk_c9
| inverse(sk_c9) = sk_c2 ),
inference(paramod,[status(thm)],[c_1934,c_792]) ).
cnf(c_4130,plain,
( identity != sk_c8
| sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_1934,c_596]) ).
cnf(c_4131,plain,
( sk_c9 != sk_c8
| sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_1934,c_4130]) ).
cnf(c_4132,plain,
( sk_c8 != sk_c9
| sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10
| sk_c9 != sk_c9 ),
inference(copy,[status(thm)],[c_4131]) ).
cnf(c_4133,plain,
( sk_c8 != sk_c9
| sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10 ),
inference(copy,[status(thm)],[c_4132]) ).
cnf(c_2434,plain,
( sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10 ),
inference(copy,[status(thm)],[c_4133]) ).
cnf(c_4134,plain,
inverse(sk_c9) = identity,
inference(paramod,[status(thm)],[c_1934,c_361]) ).
cnf(c_2487,plain,
inverse(sk_c9) = sk_c9,
inference(paramod,[status(thm)],[c_1934,c_4134]) ).
cnf(c_2488,plain,
multiply(A,sk_c9) = A,
inference(paramod,[status(thm)],[c_1934,c_302]) ).
cnf(c_4135,plain,
( multiply(sk_c9,sk_c2) = identity
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_2488,c_164]) ).
cnf(c_4136,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_1934,c_4135]) ).
cnf(c_2499,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_4136]) ).
cnf(c_2500,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_1934,c_161]) ).
cnf(c_4137,plain,
( multiply(sk_c9,sk_c6) = identity
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_2488,c_148]) ).
cnf(c_2503,plain,
( multiply(sk_c9,sk_c6) = sk_c9
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_1934,c_4137]) ).
cnf(c_2512,plain,
multiply(sk_c9,A) = A,
inference(paramod,[status(thm)],[c_1934,c_1]) ).
cnf(c_4138,plain,
( multiply(sk_c9,sk_c6) = sk_c9
| sk_c9 = sk_c2 ),
inference(paramod,[status(thm)],[c_2487,c_2318]) ).
cnf(c_4139,plain,
( sk_c6 = sk_c9
| sk_c9 = sk_c2 ),
inference(paramod,[status(thm)],[c_2512,c_4138]) ).
cnf(c_2520,plain,
( sk_c6 = sk_c9
| sk_c2 = sk_c9 ),
inference(copy,[status(thm)],[c_4139]) ).
cnf(c_4140,plain,
( multiply(inverse(sk_c9),sk_c8) = sk_c7
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_2488,c_254]) ).
cnf(c_4141,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_2487,c_4140]) ).
cnf(c_4142,plain,
( sk_c8 = sk_c7
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_2512,c_4141]) ).
cnf(c_2538,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_4142]) ).
cnf(c_4143,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_2488,c_23]) ).
cnf(c_4144,plain,
( sk_c6 = sk_c7
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_2488,c_4143]) ).
cnf(c_2728,plain,
( sk_c7 = sk_c6
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_4144]) ).
cnf(c_2731,plain,
( sk_c6 = sk_c9
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_2512,c_2503]) ).
cnf(c_4145,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_2512,c_2500]) ).
cnf(c_2733,plain,
( sk_c2 = sk_c9
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_2512,c_4145]) ).
cnf(c_2734,plain,
( sk_c2 = sk_c9
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_2512,c_2499]) ).
cnf(c_4146,plain,
( sk_c6 = sk_c8
| sk_c2 = sk_c8
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_2728,c_2538]) ).
cnf(c_2929,plain,
( sk_c6 = sk_c8
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_4146]) ).
cnf(c_4147,plain,
( sk_c2 = sk_c9
| sk_c7 = sk_c9
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_2520,c_2734]) ).
cnf(c_3157,plain,
( sk_c7 = sk_c9
| sk_c2 = sk_c9 ),
inference(copy,[status(thm)],[c_4147]) ).
cnf(c_4148,plain,
( sk_c8 = sk_c9
| sk_c2 = sk_c8
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_2929,c_2731]) ).
cnf(c_3219,plain,
( sk_c8 = sk_c9
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_4148]) ).
cnf(c_4149,plain,
( sk_c2 = sk_c9
| sk_c9 = sk_c8
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_3157,c_2733]) ).
cnf(c_4150,plain,
( sk_c2 = sk_c9
| sk_c8 = sk_c9
| sk_c2 = sk_c9 ),
inference(copy,[status(thm)],[c_4149]) ).
cnf(c_3361,plain,
( sk_c8 = sk_c9
| sk_c2 = sk_c9 ),
inference(copy,[status(thm)],[c_4150]) ).
cnf(c_4151,plain,
( sk_c8 = sk_c9
| sk_c9 = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_3361,c_3219]) ).
cnf(c_4152,plain,
( sk_c8 = sk_c9
| sk_c8 = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_4151]) ).
cnf(c_4153,plain,
( sk_c8 = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_4152]) ).
cnf(c_3522,plain,
sk_c8 = sk_c9,
inference(copy,[status(thm)],[c_4153]) ).
cnf(c_4154,plain,
( sk_c9 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10 ),
inference(paramod,[status(thm)],[c_3522,c_2434]) ).
cnf(c_3918,plain,
inverse(inverse(sk_c10)) != sk_c10,
inference(copy,[status(thm)],[c_4154]) ).
cnf(c_4155,plain,
multiply(A,sk_c9) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_301,c_2488]) ).
cnf(c_4156,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_2488,c_4155]) ).
cnf(c_4105,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_4156]) ).
cnf(c_4106,plain,
$false,
inference(resolve,[status(thm)],[c_4105,c_3918]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP256-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n011.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 14:40:58 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2243538 was started by sandbox on n011,
% 0.17/0.43 % Fri Sep 25 14:40:58 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 21.97/3.25
% 21.97/3.25 % SZS status Unsatisfiable for theBenchmark
% 21.97/3.25
% 21.97/3.25 % Proof 1 at 2.08 (+ 0.68) seconds.
% 21.97/3.25 % Length of proof is 68.
% 21.97/3.25 % Level of proof is 22.
% 21.97/3.25 % Maximum clause weight is 63.000.
% 21.97/3.25 % Given clauses 282.
% 21.97/3.25
% 21.97/3.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------